Plastic deformation processes in metals are relevant to a wide range of technological applications including manufacturing processes, energy absorption systems, and permanent fixtures. As a result, there has been tremendous efforts in developing models that can accurately describe the macroscopic behavior of metals. However a complete understanding of the kinematic hypothesis underlying these continuum models and their relationship to processes at the microscale is still lacking. The objective of this research is to revise key model assumptions in the context of crystal plasticity and to establish a more general applicable and more accurate theory. The techniques and approaches that will be used for this investigation have the potential to contribute more broadly to inelastic deformations, which is generally based on similar kinematic assumptions. This includes models of biological tissues that experience growth, damage models and viscoelasticity theories. The results of this investigation will be included in the undergraduate and graduate education and will serve as an example of interdisciplinary effort that combines mechanics with material science and applied mathematics.
The kinematics of elasto-plastic deformations in crystalline materials is very well understood at the atomistic and mesoscopic level where dislocations are fully resolved. However, the effective kinematic description at the macroscopic scale is still a topic of current debate. The research objective of this work is to rigorously derive the continuum kinematic relations describing plastic deformation from its discrete counterparts via an upscaling procedure. This goal will be achieved via a careful mathematical characterization of elasto-plastic deformations at the mesoscale and by use of homogenization techniques in the calculus of variations. The assumptions required to establish the discrete to continuum link will clearly determine the limits of applicability of the continuum relations. The development of new graduate level courses, the mentoring of students, and the targeted interaction with the peer community will contribute to the broader impact of this research.
